Alstad started her career at
Byåsen HE. In the 2006–07 season she reached the final of the
EHF Cup Winners' Cup, where they lost to Romanian
CS Oltchim Râmnicu Vâlcea. In 2013 she joined Danish side
Team Tvis Holstebro. A year later she joined league rivals
FC Midtjylland Håndbold. Here she won the
2015 Danish Championship, the 2014 Danish cup, and the 2015
EHF Cup Winners' Cup. In the final of the Danish cup she ruptured her achilles which kept her out for the rest of the season. In the summer of 2015 she returned to
Byåsen HE. Only 6 months later she joined Hungarian top team
Győri ETO KC on loan, as they were struggling with injuries. Here she won the 2016 Hungarian Championship and cup and reached the semifinal of the
EHF Champions League. The following summer she would return to
Byåsen HE for a third time. In the 2017–18 season she took a break from handball due to pregnancy leave. After the 2021–22 season she retired from handball. However, only 5 games into the 2022–23 season, she came back to the court at Byåsen.
National team She made her debut on the
Norwegian national team in 2009. At the
2009 World Women's Handball Championship she won bronze medals with the Norwegian team. A year later she won the
2010 European Championship. In 2011 she won the
2011 World Championship, followed by Gold at the
2012 Olympics. She also represented Norway at the
2013 World Championship. At the
2014 European Championship she won her second European gold. At the
2015 World Championship she won her second World Championship gold. She was not initially part of the team, and was only included during the tournament to replace the injured
Mari Molid. At the
2016 Olympics she won bronze medals with the Norwegian team, losing to Russia in the semifinals in extra time and beating Netherlands in the third place playoff. ==Achievements==